Helem Sabina Sánchez

Multiobjective tuning of PI controller using the NNC Method: Simplified problem definition and guidelines for decision making

This paper presents the application of the NNC method to the tuning of PI controllers. The main contribution is on the analysis of the tradeoff among different performance indexes as well as the need of considering the robustness as another tradeoff. Robustness has been included during last years. However, the authors do question if it is needed to include an explicit robustness measure or is better to find its correlation with another performance-like figure of merit. The use of specific compromise criteria to select an unique solution from the Pareto front generates a possibility for tuning a PI control that generates better system outputs than existing tuning methods.

Optimal Nash tuning rules for robust PID controllers

Abstract In this paper, we propose tuning rules for one degree-of-freedom proportional-integral-derivative controllers, by considering important aspects such as the trade-off in the performance in the servo and regulation operation modes and the control system robustness by constraining the maximum sensitivity peak. The different conflicting objectives are dealt with by using a multi-objective optimization algorithm to generate the trade-off optimal solutions. In this context, a simple tuning rule is determined by using the Nash solutions as a multi-criteria decision making technique. The Nash criteria is shown to provide convenient trade-off solutions for the controller tuning problem. Illustrative simulation examples show the effectiveness of the method.

Tuning rules for robust FOPID controllers based on multi-objective optimization with FOPDT models

In this paper a set of optimally balanced tuning rules for fractional-order proportional-integral-derivative controllers is proposed. The control problem of minimizing at once the integrated absolute error for both the set-point and the load disturbance responses is addressed. The control problem is stated as a multi-objective optimization problem where a first-order-plus-dead-time process model subject to a robustness, maximum sensitivity based, constraint has been considered. A set of Pareto optimal solutions is obtained for different normalized dead times and then the optimal balance between the competing objectives is obtained by choosing the Nash solution among the Pareto-optimal ones. A curve fitting procedure has then been applied in order to generate suitable tuning rules. Several simulation results show the effectiveness of the proposed approach.

Reliability based multiobjective optimization design procedure for PI controller tuning.

Abstract In this work, we propose an hybrid multi-objective optimization design procedure for PI controller tuning. This procedure focuses on reliability-based optimization instances, where Montecarlo methods are used to evaluate quantitatively the performance degradation of a controller, due to unexpected or unmodeled dynamics. The procedure is evaluated on a non-linear Peltier process. The presented results validate the procedure and its usefulness for controller tuning.

Nash-based criteria for selection of Pareto Optimal PI controller

This paper presents an approach to PI controller tuning based on an appropriate tradeoff selection from the Pareto front. The paper provides a formulation based on multiobjective optimization that analyses the tradeoff among different performance indexes. The corresponding Pareto front are generated by means of the normalized normal constraint (NNC), a numerical optimization method. As all the points from the Pareto front are compromise solutions, there is a need to select a unique solution that provides a reasonable control system. The Nash bargain solution is used for this purpose. On the basis of this selection, controller tuning rules are provided for PI controllers and First-Order-Plus-Dead-Time (FOPDT) models with normalized dead-times from 0.1 to 2.0.

Optimality Comparison of 2DoF PID Implementations.

Two-degree-of-freedom (2DoF) proportional-integrative-derivative (PID) control algorithms are presented here in order to see the conversion factors, relations and how we can improve the performance and robustness of the system. Each configuration is proposed as a multi-objective problem (MOP) it is used the Pareto front to analyze the disturbance attenuation performance versus control input usage. Examples with normalized dead-times (0.1, 1.0 and 1.75) are used to illustrate the comparison between them.

Nash tuning for optimal balance of the servo/regulation operation in robust PID control

In this paper we propose a multi-objective optimization approach for the tuning of one degree-of-freedom proportional-integral-derivative controllers where both the trade-off between the servo and regulation operation modes and the trade-off between performance and robustness are considered. After having quantified the loss of performance that occurs when robustness is taken into account in the optimal design of the controller a tuning rule is proposed based on the Nash solution. A balanced robust tuning is obtained simply starting from a first-order-plus-dead-time model of the (self-regulating) process.

Multistage procedure for PI controller design of the Boiler Benchmark problem

An multistage approach is proposed merging a deterministic and evolutionary algorithm for PI controller tuning. This technique is formulated through design of a multi-objective optimization procedure, to ensure the construction of Pareto frontier that guarantee well distribution and exclude the non-Pareto and local Pareto points. This procedure focuses on reliability-based optimization instances. To validate the approach, we will consider the Boiler Control Benchmark. The results of its usefulness for controller tuning is demonstrated.